On the Minimum Hop Count and Connectivity in One-Dimensional ad Hoc Wireless Networks

This paper investigates connectivity in one-dimensional ad hoc networks by means of the distribution of the minimum hop count between source and destination nodes. We derive the exact probability distribution of the minimum hop count from the location density of relay nodes in the multihop path selected with the Most Forward within Radius (MFR) scheme. The probability that the source and destination nodes are connected (provided by Ghasemi and Nader-Esfahani [IEEE Commun. Lett. 10(4):251–253, 2006]) can be obtained by summing the probability masses for each possible value of the minimum hop count, which provides new insights to the connectivity probability. Numerical results show the effect of the number of nodes and the transmission range on the minimum hop count.